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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Periodic point free homeomorphism of $T^ 2$
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by Michael Handel PDF
Proc. Amer. Math. Soc. 107 (1989), 511-515 Request permission

Abstract:

Suppose that $f:{T^2} \to {T^2}$ is an orientation preserving homeomorphism of the torus that is homotopic to the identity and that has no periodic points. We show that there is a direction $\theta$ and a number $\rho$ such that every orbit of $f$ has rotation number $\rho$ in the direction $\theta$.
References
  • John Franks, Recurrence and fixed points of surface homeomorphisms, Ergodic Theory Dynam. Systems 8$^*$ (1988), no. Charles Conley Memorial Issue, 99–107. MR 967632, DOI 10.1017/S0143385700009366
  • Handel, M., Zero entropy surface diffeomorphisms, preprint.
  • Michael-R. Herman, Une mĂ©thode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d’un thĂ©orème d’Arnol′d et de Moser sur le tore de dimension $2$, Comment. Math. Helv. 58 (1983), no. 3, 453–502 (French). MR 727713, DOI 10.1007/BF02564647
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 511-515
  • MSC: Primary 58F99; Secondary 57S17, 57S25
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0965243-2
  • MathSciNet review: 965243